论文标题
潜在和单调游戏的连续时间收敛率
Continuous-Time Convergence Rates in Potential and Monotone Games
论文作者
论文摘要
在本文中，我们为连续的双空游戏动力学（例如镜下降（MD）和Actor-Critic（AC）等连续时间双空游戏动力学提供了与内部NASH平衡的指数级速率。我们在$ n $ - 玩家连续的凹入游戏中进行分析，这些游戏满足某些单调性假设，同时也可能承认潜在的功能。在本文的第一部分中，我们提供了单调游戏的新颖相对表征，并表明MD及其折扣版本与$ \ Mathcal {o}（e^{ - βT}）$分别在相对强烈且相对低的单调游戏中收敛。在本文的第二部分中，我们将结果专门用于承认相对强烈的潜力的游戏，并显示AC与$ \ Mathcal {O}（e^{ - βT}）$收敛。这些速率扩展了其已知的收敛条件。进行仿真，从经验上备份了我们的结果。
In this paper, we provide exponential rates of convergence to the interior Nash equilibrium for continuous-time dual-space game dynamics such as mirror descent (MD) and actor-critic (AC). We perform our analysis in $N$-player continuous concave games that satisfy certain monotonicity assumptions while possibly also admitting potential functions. In the first part of this paper, we provide a novel relative characterization of monotone games and show that MD and its discounted version converge with $\mathcal{O}(e^{-βt})$ in relatively strongly and relatively hypo-monotone games, respectively. In the second part of this paper, we specialize our results to games that admit a relatively strongly concave potential and show AC converges with $\mathcal{O}(e^{-βt})$. These rates extend their known convergence conditions. Simulations are performed which empirically back up our results.
